Cohomology of semi-invariant submanifolds of cosymplectic manifolds
Abstract
In this paper, we study de Rham cohomology class for semi-invariant submanifolds of a cosymplectic manifold. We show that there are de Rham cohomolgy class on semi-invariant submanifold of a cosymplectic manifold. Firstly, we define semi-invariant submanifolds of a cosyplectic manifold. We present an example for semi-invariant submanifold of a cosymplectic manifold.Later, We obtain characterizations, investigate the geometry of distributions which arise from the definition of semi-invariant submanifold. We obtain that invariant distribtion is always integrable and minimal. Moreover, necessary and sufficient conditions investigate for the anti-invariant distribution to be integrable and minimal. Finally, we prove that semi-invariant submanifold of a cosymplectic manifold has nontrivial de Rham cohomology class. Further, the theoretical methodology of mathematics are used to obtain results.
Keywords
Cohomology class, cosymplectic manifold, semi-invariant submanifold
References
- Reference1 A. Bejancu, Geometry of CR-submanifolds. Dordrecht, the Netherlands, D. Reidel; 1986.
- Reference2 B.Y, Chen, Cohomology of CR-submanifolds, Annales Faculte des Sciences Toulouse, 3, (1981), 167-172.
- Reference3 D.Chinea, M. de Leon and J.C. Marrero, Topology of cosymplectic manifolds, J.Math. Pures Appl. 72, (1993), 567-591.
- Reference4 S. Deshmukh, Cohomology of CR-submanifolds of a nearly Kaehler manifold, Math. Chronicle, 16, (1982), 47-57.
- Reference5 S. Dirik, On Contact CR-Submanifolds of a Cosymplectic Manifold, Filomat, 32(13), (2018), 4787-4801.
- Reference6 F. Sahin, Cohomology of hemi-slant submanifolds of a Kaehler manifold, Journal of Advanced Studies in Topology, 5(2), (2014), 27-31.
- Reference7 T. Ghazal, Cohomology of CR-submanifolds of quasi-Kaehler manifolds, Int. J. Pure Appl. Math., 52(5), (2009), 711-715.
- Reference8 K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93-103.
- Reference9 G. Ludden, Submanifolds of cosymplectic manifold, J.Di erential Geometry, 4, (1970), 23.
- Reference10 M.Nakahara, Geometry, topology and physics, IOP Publishing, Bristol 1990.